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diff --git a/ising_scaling.tex b/ising_scaling.tex index ab5ea1b..cbd1945 100644 --- a/ising_scaling.tex +++ b/ising_scaling.tex @@ -1204,7 +1204,7 @@ the ratio. We have introduced explicit approximate functions forms for the two-dimensional Ising universal scaling function in the relevant variables. These functions are smooth to all orders, include the correct singularities, and appear to converge -exponentially to the function as they are fixed to larger polynomial order. The universal scaling function will be available in both Mathematica and Python in the supplemental material. It is implicitly defined by $\mathcal{F}_0$ and $\mathcal{F}_\pm$ in Eq.~\eqref{eq:scaling.function.equivalences.2d}, where $g(\theta}$ is defined in Eq.~\eqref{eq:schofield.funcs}, $\mathcal{F}$ in Eqs.~\eqref{eq:FfromFoFYLG}--\eqref{eq:FYL}, and the fit constants at various levels of approximation are given in Table~\ref{tab:fits}. +exponentially to the function as they are fixed to larger polynomial order. The universal scaling function will be available in both Mathematica and Python in the supplemental material. It is implicitly defined by $\mathcal{F}_0$ and $\mathcal{F}_\pm$ in Eq.~\eqref{eq:scaling.function.equivalences.2d}, where $g(\theta)$ is defined in Eq.~\eqref{eq:schofield.funcs}, $\mathcal{F}$ in Eqs.~\eqref{eq:FfromFoFYLG}--\eqref{eq:FYL}, and the fit constants at various levels of approximation are given in Table~\ref{tab:fits}. This method, although spectacularly successful, could be improved. It becomes difficult to fit the unknown functions at progressively higher order due to the complexity of the |